School Seminars and Colloquia

Random tesselations with applications to spatial communication networks

Miscellaneous Seminar
M Belz Short Course consisting of 3 lectures

by Professor Guenter Last


Institution: Universitaet Karlsruhe, Germany
Date: Wed 9th September 2009
Time: 3:15 PM
Location: various

Abstract: Lecture 2:
Wednesday, September 9, 2009: 3.15 – 5.15pm
Cussonia Court-Room 2, Old Quad

Lecture 3:
Thursday, September 10, 2009: 3.15 – 5.15pm
Old Geology-Theatre 1

Summary of the course:

A tessellation is a partition of space in non-overlapping sets (cells).
Random tessellations are a fascinating area of modern spatial stochastics with many interesting applications. These lectures aim at introducing into the theory and some applications of stationary random tessellations.

In the first lecture we will introduce and discuss the most basic chracteristics of stationary tessellations with convex cells. Our main examples will be Poisson Voronoi and Poisson hyperplane tessellations. In this case several more explicit results are available. In particular we will discuss Gamma distributions of the integral geometric contents of
(typical) faces. The second lecture is devoted to stationary tessellations with possibly non-convex cells. We will introduce and explain the concept of a balanced partition and its relationship to invariant transports of random measures. In the third lecture we will apply and extend the theory to spatial models of wireless communication networks, an area that is in great need of stochastic geometry tools.

For More Information: contact Kostya Borovkov. email borovkov@unimelb.edu.au